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NumericalAlgebraicGeometry :: randomInitialPair

randomInitialPair -- a random initial pair

Synopsis

Description

Generates a start system S that has an equal chance of reaching any of the solutions of the target system T. For more details see: C. Beltran and A. Leykin, "Certified numerical homotopy tracking", arXiv:0911.1783

i1 : T = randomSd {2,3};
i2 : (S,solsS) = randomInitialPair T

                                2                                            
o2 = ({(.0548523 + .243801*ii)x1  + (- .330049 - .01444*ii)x1*x2 + (- .172922
     ------------------------------------------------------------------------
                    2                                               
     + .186318*ii)x2  + (- .0459481 - .142314*ii)x1*x3 + (.0089593 +
     ------------------------------------------------------------------------
                                                  2            
     .0870104*ii)x2*x3 + (.092786 + .0397301*ii)x3 , (.110607 -
     ------------------------------------------------------------------------
                  3                            2                 
     .271955*ii)x1  + (.0653142 + .134106*ii)x1 x2 + (- .623817 -
     ------------------------------------------------------------------------
                     2                             3               
     .117291*ii)x1*x2  + (- .374627 - .380549*ii)x2  + (- .153372 +
     ------------------------------------------------------------------------
                 2                                                 
     .03405*ii)x1 x3 + (.587187 + .819856*ii)x1*x2*x3 + (.0258006 +
     ------------------------------------------------------------------------
                  2                                    2             
     .201962*ii)x2 x3 + (- .0229733 - .0662603*ii)x1*x3  + (.155945 -
     ------------------------------------------------------------------------
                     2                            3
     .262864*ii)x2*x3  + (.229697 - .0714141*ii)x3 }, {{.74294+.109814*ii,
     ------------------------------------------------------------------------
     .0849934+.31294*ii, .546453+.179485*ii}})

o2 : Sequence
i3 : M = track(S,T,solsS,gamma=>0.6+0.8*ii,Software=>M2)

o3 = {{.878232+.167967*ii, -.170467-.190516*ii, .358132+.0829506*ii}}

o3 : List

See also

Ways to use randomInitialPair :